Log of Both Sides TheoremIf A, B, and b are positive real numbers
with b not equal to 1, then
logbA = logbB
is equivalent to A = b.

Logarithmic EquationsLog Type I: The unknown is the logarithm.Log Type II: The unknown is the base.Log Type III: The logarithm of an unknown is
equal to a number.Log Type IV: The logarithm of an unknown is equal
to the logarithm of a number.

Laws of Logarithms Let A, B, and b be positive numbers
(b not equal to 1) and let p be any real number,
First law (Additive):
logb(AB) = logbA + logbB
Second law (Subtractive):
logb(A/B) = logbA
+ logbB
Third law (Multiplicative):
logb(A)p
= P logbA